# Cart on a Ramp

Topics: Kinematics, Acceleration, Derivative Pages: 9 (2798 words) Published: August 26, 2012
Objectives: To learn about motion through studying and matching graphs of position vs. time and velocity vs. time; to develop an understanding of the concepts of kinematics. Predict, sketch, and test motion graphs to better understand motion.

Equipment: Computer
Vernier computer interface
Logger Pro
Vernier Motion Detector
Meter stick

Preliminary Questions:
1a.
The pink line shows the position of an object at rest with respect to time. POSITION

TIME

1b. The pink line shows the position of an object moving in the positive direction at constant speed with respect to time. POSITION

TIME

POSITION
1c. The pink line shows the position of an object moving in the negative direction at constant speed with respect to time.

TIME

POSITION
1d.
The pink line shows the object accelerating at a constant, steady speed. The blue line shows an object that is accelerating at a less constant speed, slowly at first, then increasing speed. TIME

2a. The pink line is on the x-axis (zero) with respect to time because velocity is zero when an object is at rest. VELOCITY

TIME

VELOCITY
2b.
The pink line is at ¾ position because that is the slope of the graph of 1b. above. The line is flat because of constant speed.

TIME

VELOCITY

2c. The pink line is at – ¾ because that is the slope of the graph of 1c. above. TIME

2d.

VELOCITY
The pink line shows the velocity with respect to time of the of the pink line from graph 1d. TIME

Procedure: Part I
1. We obtained all the materials necessary for this lab and assembled them: we taped off four one-meter increments, connected the motion detector to the interface to the computer, and opened Logger Pro. 2. We then placed the motion detector on the tabletop, facing the four-meter open space. 3. Using Logger Pro’s 1a Graph Matching file, we used the collect button to begin experimenting with motion. 4. We walked slowly away from the detector and obtained a steadily increasing slope (1a. below).

1a.

5. We tried this again, but walked faster and obtained a steadily increasing slope that was steeper (2a. below)

2a.

6. Experimenting with motion, we matched more graphs to those we already sketched from the Preliminary Questions. For the first one, we stood there to get the straight line (stationary object). Part II: Position vs. Time Graph Matching

7. Opening 1b Graph Matching from Logger Pro, we got a position vs. time graph. 8. To match this graph, we had a lab partner begin by standing still for 1 sec., then walk quickly but steadily for 2 sec., then stop again for 3 sec., then walk back towards the detector for 1.5 sec., and finally, stop for about 3 more sec. 9. This worked out a lot better in theory than in our experiment. To match this graph, we had to try many times because of jerky movements, spikes in the graph, and unsteady speed increases. 10. We then opened a new target graph, 1c Graph Matching, and repeated the above steps to match the new graph. 11. Recognizing how to match the target graph was easier now; the hard part was to get rid of the spikes in our motion and to match, more closely, the speed in the graphs. Part III: Velocity vs. Time Graph Matching

12. We opened the file 1d Graph Matching to get a velocity vs. time graph. 13. To match this graph, we would have to begin by not moving at the 0 meter mark for 2 sec. then step quickly to .5 meters and stop again for 3 sec. then step forwards towards the detector .5 meters quickly and stop again fro 3 sec. Then, step towards the detector another .5 meters and stop for 3 sec. 14. To check our predictions, we tried matching this trial many times and got the general shape but increasing velocity in a split second to match the step part...